A linearized non-rigid MHD consistent displacement model is shown to be adequate to the study of the vertical stability of a plasma in an air core or iron core tokamak. This simple but accurate approach, which can be extended to the study of shape and radial position control, can be used in determining the limits of validity of the linear approximation and simulating the behaviour of a detection system based on a set of flux measurements. The method provides a basis for the optimization of position measurements and feedback parameters. The features of the model are illustrated, with reference to the study of the vertical stability of a NET configuration, showing the significance of the choice of the input signal.